Gravity from entropy

Since the discovery of the thermodynamics of black holes, a central challenge has been uniting statistical mechanics with gravity and quantum information. Here I illustrate the  new Gravity from Entropy [1] approach to quantum gravity whose Lagrangian is given by the geometric quantum relative entropy. This framework recovers Einstein’s equations in the low energy small curvature limit and predicts modified gravity beyond. In Gravity from Entropy the action is expressed in terms of a new field, the G-field. This field dresses the true metric and is responsible for the emergence of a small and positive cosmological constant. From the Gravity from Entropy action the area law for the entropy the Schwarzschild black holes is recovered in the limit of large Schwarzschild radius [2].

[1] Bianconi, G., 2025. Gravity from entropy. Physical Review D, 111(6), p.066001.

[2] Bianconi, G., 2025. The quantum relative entropy of the Schwarzschild black hole and the area law. Entropy, 27(3), p.266.